The singular fibre of the Hitchin map

Abstract

Given any line bundle L of positive degree, on a compact Riemann surface, let $M_L^{\Lambda }$ be the moduli space of L-twisted Higgs pairs of rank 2 with fixed determinant isomorphic to $\Lambda$ and traceless Higgs field. We give a description of the singular fibre of the Hitchin map $H:M_{\Lambda }^L\to H^0(L^2)$, when the corresponding spectral curve has any singularity of type $A_{m-1}$. In particular, we prove directly that this fibre is connected.

28 pages; v3; minor changes: added Proposition 3.7 and main Theorem 8.1 now also refers the fibre over zero; final version

References in corpus (1)

• Fibration de Hitchin et endoscopie

Cited by in corpus (5)

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• Monodromy of the SL_2 Hitchin fibration
• Rank two quadratic pairs and surface group representations
• Semi-abelian spectral data for singular fibres of the $\mathsf{SL}(2,\mathbb{C})$-Hitchin system
• The Algebraic and Analytic Compactifications of the Hitchin Moduli Space